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Non-homogeneous Markov chains with a finite state space and a Doeblin type theorem. (English) Zbl 0818.60059

Summary: W. Doeblin [Publ. Fac. Sci. Univ. Masaryk 236, 3-13 (1937; Zbl 0016.41102)] considered some classes of finite state nonhomogeneous Markov chains and studied their asymptotic behavior. Later H. Cohn [Adv. Appl. Probab. 13, 388-401 (1981; Zbl 0469.60065)] considered another class of such Markov chains (not covered earlier) and obtained Doeblin type results. Though this paper does not present the “best possible” results, the method of proof will be of interest to the reader. It is elementary and based on J. Hajnal’s results on products of nonnegative matrices [Math. Proc. Cambridge Philos. Soc. 79, 521-530 (1976; Zbl 0333.15013)].

MSC:

60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
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